In this presentation, we describe the computation of higher-order QED effects relevant in hadronic collisions. In particular, we discuss the calculation of mixed QCD-QED one-loop contributions to the Altarelli-Parisi splittings functions, as well as the pure two-loop QED corrections. We explain how to extend the DGLAP equations to deal with new parton distributions, emphasizing the consequences of the novel corrections in the determination (and evolution) of the photon distributions.
Recent improvements in the low energy e+e- annihilation data and their influence on the determination of the hadronic contribution to the running of the QED fine structure constant at m_Z are discussed. Using CMD-2 and KLOE measurements in the rho region we obtain Delta alpha(5)_had(s) = 0.02758 +/- 0.00035 at s = m_Z^2.
Compact analytical formulae for QED radiative corrections in the processes of elastic $e-p$ scattering are obtained in the case when kinematic variables are reconstructed from the recoil proton momentum measured. Numerical analysis is presented under kinematic conditions of current experiments at JLab.
We review the theory of hadronic atoms in QCD + QED, based on a non-relativistic effective Lagrangian framework. We first provide an introduction to the theory, and then describe several applications: meson-meson, meson-nucleon atoms and meson-deuteron compounds. Finally, we compare the quantum field theory framework used here with the traditional approach, which is based on quantum-mechanical potential scattering.
An update is described of a model independent method to determine the hadronic contribution to the QED running coupling at the Z-boson mass scale, $Δα_{\text{HAD}}(M_{Z}^{2})$. The major source of uncertainty is from the contribution of the light quark vector current correlator at zero momentum. This uncertainty is substantially reduced using recently improved lattice QCD results for this correlator. The result is $Δα_{\text{HAD}}(M_{Z}^{2})=274.13 (0.73)\, \times 10^{-4}$.
We review some recent results about the computation of mixed QCD-QED corrections beyond the leading order in perturbation theory. We start by considering the effects induced in the Altarelli-Parisi equations and the partonic distributions. In particular, we describe the computation of one-loop mixed QCD-QED and two-loop QED terms in the splitting kernels, which are relevant to account for the presence of photon distributions. In the last part, we briefly talk about the implementation of these corrections in the context of the $q_T$-subtraction/resummation formalism.
A numerical analysis of QED radiative corrections for elastic e(mu)p cattering in hadronic variables at energies of the current experiment at JLab is performed. The explicit formulas from the review of Akhundov et al. resulting from the integration over the phase space of leptonic variables plus photon are used to obtain the values of the cross sections and the radiative correction factor for unpolarized lepton-proton scattering. Our numerical results agree with the corresponding results arising from the formulas of Afanasev et al.
In this paper we investigate the photoproduction of QED bound states in proton -- proton, proton -- nucleus and nucleus -- nucleus collisions at RHIC, LHC and FCC energies considering an accurate treatment of the absorptive corrections and for the nuclear form factor. The total cross sections for the production of singlet and triplet $(l^+ l^-)$ states, with $l = e,\, μ, \, τ$, are estimated and a detailed analysis of the photoproduction of singlet QED bound states is performed considering the rapidity ranges covered by central and forward detectors. The impact of the Coulomb corrections on th…
I review recent evaluations of the hadronic contributions to the muon anomalous magnetic moment (g-2)_mu and to the effective fine structure constant alpha (M_Z). A new estimate for the hadronic shift delta_alpha hadronic = 0.027782 +/- 0.000254 is presented which implies 1/alpha (M_Z) = 128.913 +/- 0.035. It is based on a recent perturbative calculation of the Adler function which includes mass effects up to three-loops in a MOM scheme and requires little ad hoc assumptions. I then discuss perspectives for possible improvements in estimations of g-2 which we expect from the Phi--factory DAPHN…
We use recently evaluated radiative and nonperturbative corrections to production of heavy quarks by a vector current to give very precise theoretical calculations of the high energy ($t^{1/2}\geq \sqrt{2}$ GeV) imaginary part of the photon vacuum polarization function, ${\rm Im}Π(t)$. This allows us to improve the corresponding contributions to the muon (or any other lepton) $g-2$ anomaly and to the running QED constant on the $Z$, $\barα_{\rm QED}(M_Z)$. This decreases the error in the evaluations by a factor between two and six for the high energy contribution, and by some 50\% for the over…
I review recent estimates of the non-perturbative hadronic vacuum polarization contributions. Since these at present can only be evaluated in terms of experimental data of limited precision, the related uncertainties pose a serious limitation in our ability to make precise predictions. Besides e+e- - annihilation data also tau decay spectra can help to get better predictions. Here, it is important to account for all possible iso-spin violations in tau - decay spectra, from which e+e- cross sections may be obtained by an iso-spin rotation. The observed 10% discrepancy in the region above the rh…
We consider the transverse-momentum ($q_T$) distribution of $Z$ bosons produced in hadronic collisions. At small values of $q_T$, we perform the analytic resummation of the logarithmically enhanced QED contributions up to next-to-leading logarithmic accuracy, including the mixed QCD-QED contributions at leading logarithmic accuracy. Resummed results are consistently matched with the next-to-leading fixed-order results (i.e. $\mathcal{O}(α^2)$) at small, intermediate and large values of $q_T$. We combine the QED corrections with the known QCD results at next-to-next-to-leading order ($\mathcal{…
Theoretical predictions for Bhabha scattering at the two-loop level require the inclusion of hadronic vacuum polarization in the photon propagator. We present predictions for the contributions from reducible amplitudes which are proportional to the vacuum polarization $π(q^2)$ and from irreducible ones where the vacuum polarization appears in a loop representing vertex or box diagrams. The second case can be treated by using dispersion relations with a weight function proportional to the $R$-ratio as measured in electron-positron annihilation into hadrons and kernels that can be calculated per…
Isospin is an almost exact symmetry of strong interactions and the corrections to the isosymmetric limit are, in general, at the percent level. For several hadronic quantities relevant for flavour physics phenomenology, such as pseudoscalar meson masses or the kaon leptonic and semileptonic decay rates, these effects are of the same order of magnitude of the uncertainties quoted in current large-scale QCD simulations on the lattice and cannot be neglected anymore. In this contribution I discuss some recent results for the leptonic decay rates of light pseudoscalar mesons obtained by the Soton-…
The anomalous magnetic moment of the muon $a_μ$ is one of the most accurate quantities in Particle Physics. The long-standing discrepancy of about $3.7$ standard deviations between the experimental value and the prediction of the Standard Model could represent an intriguing indication of New Physics. The experiments at Fermilab (E989) and at J-PARC (E34) aim at reducing significantly the experimental uncertainty, thus making the theoretical one due to hadronic corrections the main limitation of this stringent test of the Standard Model. In this contribution we present the results of a first-pr…
When aiming at the percent precision in hadronic quantities calculated by means of lattice simulations, isospin breaking effects become relevant. These are of two kinds: up/down mass splitting and electromagnetic corrections. In order to account properly for the latter, a consistent formulation of electrically-charged states in finite volume is needed. In fact on a periodic torus Gauss law and large gauge transformations forbid the propagation of electrically-charged states. In this talk I will review methods that have been used or proposed so far in order to circumvent this problem, while hig…
The form factor that yields the light-by-light scattering contribution to the muon anomalous magnetic moment is computed in lattice QCD+QED and QED. A non-perturbative treatment of QED is used and is checked against perturbation theory. The hadronic contribution is calculated for unphysical quark and muon masses, and only the diagram with a single quark loop is computed. Statistically significant signals are obtained. Initial results appear promising, and the prospect for a complete calculation with physical masses and controlled errors is discussed.
We introduce a model independent method for the determination of the hadronic contribution to the QED running coupling, $Δα_{\text{HAD}}(M_{Z}^{2})$, requiring no $e^+e^-$ annihilation data as input. This is achieved by calculating the heavy-quark contributions entirely in perturbative QCD, whilst the light-quark resonance piece is determined using available lattice QCD results. Future reduction in the current uncertainties in the latter shall turn this method into a valuable alternative to the standard approach. Subsequently, we find that the precision of current determinations of $Δα_{\text{…
In this paper, for the first time a method is proposed to compute electromagnetic effects in hadronic processes using lattice simulations. The method can be applied, for example, to the leptonic and semileptonic decays of light or heavy pseudoscalar mesons. For these quantities the presence of infrared divergences in intermediate stages of the calculation makes the procedure much more complicated than is the case for the hadronic spectrum, for which calculations already exist. In order to compute the physical widths, diagrams with virtual photons must be combined with those corresponding to th…
Recently, the Budapest-Marseille-Wuppertal collaboration achieved sub-percent precision in the evaluation of the lowest-order hadronic vacuum polarization contribution to the muon $g_μ-2$ (arXiv:hep-lat/2002.12347v3). At this level of precision, isospin-symmetric QCD is not sufficient. In this contribution we review how QED and strong-isospin-breaking effects have been included in our work. Isospin breaking is implemented by expanding the relevant correlation functions to second order in the electric charge $e$ and to first order in $m_u-m_d$. The correction terms are then computed using isosp…
We reevaluate the hadronic contribution to the running of the QED fine structure constant alpha(s) at s = M_Z^2. We use data from e+e- annihilation and tau decays at low energy and at the qq-bar thresholds, where resonances occur. Using so-called spectral moments and the Operator Product Expansion (OPE), it is shown that a reliable theoretical prediction of the hadronic production rate R(s) is available at relatively low energies. Its application improves significantly the precision on the hadronic vacuum polarization contribution. We obtain delta_alpha^had = (277.8 +/- 2.6) x 10^-4 yielding a…
Within the standard V - A theory of weak interactions, Quantum Electrodynamics (QED) and the linear sigma-model (LsM) of strong low-energy hadronic interactions we analyse gauge and infrared properties of hadronic structure of the neutron and proton in the neutron beta decay to leading order in the large nucleon mass expansion. We show that the complete set of Feynman diagrams describing radiative corrections of order O(α/π), induced by hadronic structure of the nucleon, to the rate of the neutron beta decay is gauge non-invariant and unrenormalisable. We show that a gauge non-invariant contri…
In order to reach (sub-)per cent level precision in lattice calculations of the hadronic vacuum polarisation, isospin breaking corrections must be included. This requires introducing QED on the lattice, and the associated finite-size effects are potentially large due to the absence of a mass gap. This means that the finite-size effects scale as an inverse polynomial in $L$ rather than being exponentially suppressed. Considering the $\mathcal{O}(α)$ corrected hadronic vacuum polarisation in QED$_{\mathrm{L}}$ with scalar QED as an effective theory, we show that the first possible term, which is…
We study the potential impact on the electroweak (EW) fits due to the tensions between the current determinations of the hadronic vacuum polarisation (HVP) contributions to the anomalous magnetic moment of the muon ($a_μ$), based on either phenomenological dispersion integrals using measured hadronic spectra or on Lattice QCD calculations. The impact of the current tension between the experimental measurement of $a_μ$ and the total theoretical prediction based on the phenomenological calculations of the HVP are also studied. The correlations between the uncertainties of the theoretical predict…
The ratios among the leading-order (LO) hadronic vacuum polarization (HVP) contributions to the anomalous magnetic moments of electron, muon and tau-lepton, $a_{\ell=e,μτ}^{HVP,LO}$, are computed using lattice QCD+QED simulations. The results include the effects at order $O(α_{em}^2)$ as well as the electromagnetic and strong isospin-breaking corrections at orders $O(α_{em}^3)$ and $O(α_{em}^2(m_u-m_d))$, respectively, where $(m_u-m_d)$ is the $u$- and $d$-quark mass difference. We employ the gauge configurations generated by the Extended Twisted Mass Collaboration with $N_f=2+1+1$ dynamical q…
Within the standard V - A theory of weak interactions, Quantum Electrodynamics (QED) and the linear sigma-model (LsM) of strong low-energy hadronic interactions we analyse gauge properties of hadronic structure of the neutron and proton in the neutron radiative beta-decay. We show that the Feynman diagrams, describing contributions of hadronic structure to the amplitude of the neutron radiative beta-decay in the tree-approximation for strong low-energy interactions in the LsM, are gauge invariant. In turn, the complete set of Feynman diagrams, describing the contributions of hadron-photon inte…
Within the standard V - A theory of weak interactions, Quantum Electrodynamics (QED) and the linear sigma-model (LsM) of strong low-energy hadronic interactions we analyse infrared properties of hadronic structure of the neutron and proton in the neutron beta decays to leading order in the large nucleon mass expansion. We confirm validity and high confidence level of contributions of hadronic structure of the nucleon to the radiative corrections, calculated by Sirlin (Phys. Rev. 164, 1767 (1967)) to leading order in the large nucleon mass expansion. At the level of order 10^{-5} relative to Si…
Control over quantum electrodynamics (QED) radiative corrections is critical for precise determination of neutrino oscillation probabilities from observed (anti)neutrino detection rates. It is particularly important to understand any difference between such corrections for different flavors of (anti)neutrinos in charged-current interactions. We provide theoretical foundations for calculating these corrections. Using effective field theory, the corrections are shown to factorize into soft, collinear, and hard functions. The soft and collinear functions contain large logarithms in perturbation t…
PSI Center for Neutron and Muon Sciences（保罗谢勒研究所中子与μ子科学中心）；Physik-Institut, Universität Zürich（苏黎世大学物理学院）；Università degli Studi di Torino & INFN（都灵大学及意大利国家核物理研究所）；University of Liverpool（利物浦大学）
We present disperon QED, a method to deal with data input in loop processes in Monte Carlo codes. It relies on dispersion relations, automated tools such as OpenLoops, effective field theory methods and a threshold subtraction. We motivate this method and apply it to the process $ee\toππ$ in McMule to deal with hadronic vacuum polarisation insertions in two-loop contributions as well as the vector form factor of the pion within the form-factor scalar QED approximation. The generality of this method for more complicated processes is emphasised.
We give an exhaustive presentation of the semi-analytical approach to the model independent leptonic QED corrections to deep inelastic neutral current lepton-nucleon scattering. These corrections include photonic bremsstrahlung from and vertex corrections to the lepton current of the order ${\cal O}(α)$ with soft photon exponentiation. % A common treatment of these radiative corrections in several variables -- leptonic, hadronic, mixed, Jaquet-Blondel variables -- has been developed and double differential cross-sections are calculated. In all sets of variables we use some structure functions,…
A new result for the hadronic vacuum polarization correction to the muonium hyperfine splitting (HFS) is presented: Delta nu(had - vp) = (0.233 +- 0.003) kHz. Compared with previous calculations, the accuracy is improved by using the latest data on e+e- -> hadrons. The status of the QED prediction for HFS is discussed.
We compute the QCD$\times$QED (${\cal{O}}(α_s α)$) mixed and QED$^2$ (${\cal{O}}(α^2)$) corrections to the production of an on-shell $Z$ boson in hadronic collisions. We obtain them by profiting from the calculation of the pure QCD terms after taking the corresponding abelian limits. Therefore, we extend the available knowledge up to complete next-to-next-to leading order precision in QCD$\oplus$QED. We present explicit results for the perturbative coefficients and perform the phenomenological analysis at different collider energies with particular emphasis on the mixed corrections. We study t…
This manual describes version 1.0 of the Monte Carlo event generator KROWIG for deep inelastic lepton hadron scattering at HERA. KROWIG combines the implementation of QED radiative corrections in KRONOS with the QCD parton showers and cluster fragmentation of HERWIG.
We review the theory of hadronic atoms in QCD+QED. The non-relativistic effective Lagrangian approach, used to describe this type of bound states, is illustrated with the case of pi+pi- atoms. In addition, we discuss the evaluation of isospin-breaking corrections to hadronic atom observables by invoking chiral perturbation theory.
We present a first-principles lattice QCD+QED calculation at physical pion mass of the leading-order hadronic vacuum polarization contribution to the muon anomalous magnetic moment. The total contribution of up, down, strange, and charm quarks including QED and strong isospin breaking effects is found to be $a_μ^{\rm HVP~LO}=715.4(16.3)(9.2) \times 10^{-10}$, where the first error is statistical and the second is systematic. By supplementing lattice data for very short and long distances with experimental R-ratio data using the compilation of Ref. [1], we significantly improve the precision of…
In this article, general properties of impact factors involved in jet-like QED processes are explored. In particular, a general link is established between their helicity properties and their order of magnitude as defined by jet-like kinematics. Exact results are given for some processes in the strict forward direction and a general method is proposed to track orders in the calculation of multi-bremsstrahlung processes.
Effects of vacuum polarization by hadronic and heavy-fermion insertions were the last unknown two-loop QED corrections to high-energy Bhabha scattering and have been first announced in \cite{Actis:2007fs}. Here we describe the corrections in detail and explore their numerical influence. The hadronic contributions to the virtual O(alpha^2) QED corrections to the Bhabha-scattering cross-section are evaluated using dispersion relations and computing the convolution of hadronic data with perturbatively calculated kernel functions. The technique of dispersion integrals is also employed to derive th…
Reaching the desired precision level for W and Z processes at the LHC will require a mixture of higher-order QCD and electroweak corrections. HERWIRI2 is a step in implementing QED x QCD exponentiation in a hadronic event generator. This program implements leading electroweak corrections and coherent exclusive exponentiation in a HERWIG environment. We discuss the status of the program, recent tests, and future developments.
In the paper, we study the properties of the $Z$-boson hadronic decay width by using the $\mathcal{O}(α_s^4)$-order quantum chromodynamics (QCD) corrections with the help of the principle of maximum conformality (PMC). By using the PMC single-scale approach, we obtain an accurate renormalization scale-and-scheme independent perturbative QCD (pQCD) correction for the $Z$-boson hadronic decay width, which is independent to any choice of renormalization scale. After applying the PMC, a more convergent pQCD series has been obtained; and the contributions from the unknown $\mathcal{O}(α_s^5)$-order…
The bulk of large radiative corrections to any process can be obtained by promoting coupling constants to be running ones and by including QED radiation at the leading logarithmic level via structure functions evoluted at some scale. The problem of fixing the proper scale in running coupling constants and in structure functions for non-annihilation processes is briefly addressed and the general solution is analyzed.
In these lecture notes the basics of QED corrections to hadronic decays are reviewed with special emphasis on conceptual (e.g. counting and tracking of infrared sensitive logs) rather than numerical aspects. General matters are illustrated for the cases of increased complexity and decreased inclusiveness: $e^+ e^- \to hadrons$, the leptonic decay $π^+ \to \ell^+ \bar ν$ and the semileptonic decay $B \to π\ell^+ \bar ν$. The non-trivial and ongoing efforts of including structure dependence are very briefly outlined.
On account of its application to the present and future analysis of the virtual photon correction to the hadronic properties by means of lattice QCD simulation, we initiate the study of the finite size scaling effect on the QED correction using low energy effective theory of QCD with QED. For this purpose, we begin with formulating a new QED on the space with finite volume. By adapting this formalism to the partially quenched QCD with electromagnetism, we explore the qualitative features of the finite size scaling effect on the electromagnetic correction to the masses of pseudo-Goldstone boson…
QED processes at electron-positron colliders are considerd. We present differential cross-sections for large-angle Bhabha scattering, annihilation into muons and photons. Radiative corrections in the first order are taken into account exactly. Leading logarithmic contributions are calculated in all orders by means of the structure-function method. An accuracy of the calculation can be estimated about 0.2%.
I present a preliminary calculation of the hadronic vacuum polarization for 2+1 flavors of improved Kogut-Susskind quarks by utilizing a set of gauge configurations recently generated by the MILC collaboration. The polarization function $Π(q^2)$ is then used to calculate the lowest order (in $α_{QED}$) hadronic contribution to the muon anomalous magnetic moment.
Inelastic QED processes, the cross sections of which do not drop with increasing energy, play an important role at high-energy colliders. Such reactions have the form of two-jet processes with the exchange of a virtual photon in the t-channel. We consider them in the region of small scattering angles $m/E \lesssim θ\ll 1$, which yields the dominant contribution to their total cross sections. A new effective method is presented and applied to QED processes with emission of real photons to calculate the helicity amplitudes of these processes. Its basic idea is similar to the well-known equivalen…
The calibration QED process cross sections for experiments on planned electron-photon and photon-photon colliders for detecting the small angles scattered particles are calculated. These processes describe the creation of two jets moving sufficiently close to the beam axis directions. The jets containing two and three particles including charged leptons, photons and pseudoscalar mesons are considered explicitly. Considering the pair production subprocesses we take into account both bremsstrahlung and double photon mechanisms. The obtained results are suitable for further numerical calculations…
We propose a new set of measurements which can be performed at the LHC using roman pot detectors. This new method is based on exploiting excitation curves to measure kinematical properties of produced particles. We illustrate it in the case of central diffractive W pair production.
High energy scattering processes of charged particles are accompanied by radiation of hard photons. Emission collinear to the incident particles, which leads to a reduction of the effective beam energy, and the possibility to directly measure these photons at the HERA electron-proton collider provides important physics opportunities. For deep inelastic scattering, the measurement of radiative processes extends the kinematic range accessible to the HERA experiments to lower Q^2, as well as helps in separating the proton structure functions without the need to run at different collider energies.…
We determine the contribution to the anomalous magnetic moment of the muon from the $α^2_{\mathrm{QED}}$ hadronic vacuum polarization diagram using full lattice QCD and including $u/d$ quarks with physical masses for the first time. We use gluon field configurations that include $u$, $d$, $s$ and $c$ quarks in the sea at multiple values of the lattice spacing, multiple $u/d$ masses and multiple volumes that allow us to include an analysis of finite-volume effects. We obtain a result for $a_μ^{\mathrm{HVP,LO}}$ of $667(6)(12)$, where the first error is from the lattice calculation and the secon…
It is a well-known fact that, among the electroweak corrections, QED radiation gives the largest contribution and the needed precision requires a re-summation of the large logarithms which show up in perturbation theory. For two fermion annihilation processes initial state radiation is a definable, gauge-invariant, concept and one has general tools to deal with it; the structure function approach and also the parton-shower method. However, when one tries to apply the algorithm to four-fermion processes that include non-annihilation channels a problem is faced: is it still possible to include Q…
We consider inelastic QED processes, the cross sections of which do not drop with increasing energy. Such reactions have the form of two-jet processes with the exchange of a virtual photon in the t-channel. We consider them in the region of small scattering angles m/E <= theta << 1, which yield the dominant contribution to their cross sections. A new effective method is presented to calculate the corresponding helicity amplitudes. Its basic idea consists in replacing spinor structures for real and weakly virtual intermediate leptons by simple transition vertices for real leptons. The obtained …
As continuation of our previous paper we further develop our new method for calculating helicity amplitudes of jet-like QED processes described by tree diagrams, applying it to lepton pair production. This method consists in replacing spinor structures for real and weakly virtual intermediate leptons by simple transition vertices. New vertices are introduced for the pair production case, and previous bremsstrahlung vertices are generalized to include virtual photons inside the considered jet. We present a diagrammatic approach that allows to write down in an efficient way the leading helicity …
A derivation of fully polarization-resolved probabilities is provided for high-energy photon emission and electron-positron pair production in ultrastrong laser fields. The probabilities resolved in both electron spin and photon polarization of incoming and outgoing particles are indispensable for developing QED Monte Carlo and QED-Particle-in-Cell codes, aimed at the investigation of polarization effects in nonlinear QED processes in ultraintense laser-plasma and laser-electron beam interactions, and other nonlinear QED processes in external ultrastrong fields, which involve multiple elementa…
In this work we extend the $q_T$-subtraction formalism, originally developed for QCD corrections, to the case of mixed QCD$\otimes$QED corrections, and apply it to the fully exclusive calculation of the ${\cal{O}}(α_sα)$ contribution to the production of an off-shell $Z$ boson in hadronic collisions. We present explicit results for the subtraction term and the hard factor, therefore providing all the ingredients needed for the application of the formalism up to ${\cal{O}}(α_sα)$. To study the phenomenological impact we consider the decay of the off-shell $Z$ boson into a pair of neutrinos, and…
